# How to find the average over an area of center for a given radius

I have an excel file which contains the lat and long values of the center of a Tropical Cyclone(TC). The excel file is as given below:

19.8  69.4
20    69
20.4  68.2
20.5  67.2
20.5  65.7
20.3  65
20.2  64.2
20.2  63.7
20.2  62.9
20.2  62.3
20.2  61.5
20.1  61
20.1 60.3
20    59.5
19.9  58.9
19.8  58.3


Also, I have an NC(NetCDF) file which is of that of air temperature(The link to the data is given)air_temp.nc. Now what I intend to do is average over an area of radius 2.5◦ on the storm center for the variable in the NC data i.e. for each lat long value I need to find the average over an area of average 2.5◦. I know how to find the simple average using NumPy mean for individual lat-long, but I am confused about how to find over an area for a given radius.

• you have a latitude and longitude in TC data and you have a latitude and longitude in NC data. You want to find out mean of what value ? What is the column name which contains values whose mean is to be found out ? May 14, 2020 at 8:52
• @Simple Guy, I need to find the mean of the variable present in the NC data. It will be named as airtemp May 14, 2020 at 9:04
• See my answer below May 14, 2020 at 13:56

I think your problem is not so much calculating the average, as it is to create a subset within a radius. Once you have that subset, calculating the average is trivial.

Note however that that example works with a 2d circle, which isn't exactly what you are looking for because Earth is a globe. In order to adjust for it, you'll need the great circle distance (or Haversine distance). Why? Look here: https://en.wikipedia.org/wiki/Haversine_formula

You'll find a python implementation of that concept here: https://stackoverflow.com/questions/52889566/calculate-euclidean-distance-for-latitude-and-longitude-pandas-dataframe-pytho

# 1. Load the data into a dataframe

import pandas as pd
import xarray as xr

data = xr.open_dataset('file')
df = data.to_dataframe()

• @S van Balen thanks for the suggestion you have given. I have gone through both the examples but I am not able to interpret both as I am new in using python, so if you can help by showing how to use both in my problem it will be much appreciated... May 12, 2020 at 16:36
• Do you already have a data frame up an running with the values loaded? If so could you add it to the question. If you don't know how to do that, let me know! May 13, 2020 at 8:21
• @S van Balen I dont know how to do that. Can you please show how to do that May 13, 2020 at 8:44
• Ok I'll add it to my answer because comments don't allow enough formatting. Please comment further questions, I'll add them step by step. May 13, 2020 at 9:17
• @S van Balen ok values loaded. Now next what to do? May 13, 2020 at 9:44

Define a function to calculate distance between two latitudes and longitudes. I found php implementation of below here. I converted it to python.

import numpy as np
import math

def getDistanceBetweenPoints(latitude1, longitude1, latitude2, longitude2):
theta = longitude1 - longitude2

distance = math.acos(distance)
distance = np.degrees(distance)

return distance


Import TC data in the pandas dataframe and apply below function to call on the DataFrame. The function would call above function getDistanceBetweenPoints for each latitude and longitude

# create a dataframe
df = pd.DataFrame(tc_csv_file_path)

# take subset of the data frame with columns we want
df_lat_long = df[['latitude', 'longitude']]

# insert a new column in dataframe which would hold distance between the latitudes and longitudes
df_lat_long.insert(df_lat_long.shape, "distance", [0.0 for val in range(df_lat_long.shape)], True)


Define a function which would be invoked row wise on a data frame

def getDistanceBetweenPoints_df(row):
# Place latitude/longitude for a centre point here
# I have filled 0.0, you replace with with actual values
centre_lat = 0.0
centre_long = 0.0
row['distance'] = getDistanceBetweenPoints(centre_lat, centre_long, row['longitude'], row['latitude'], unit='Km')


Now invoke this function on data frame. It will called row wise and it will populate the column distance in the dataframe with the distance between center latitude/longitude and the row's latitude/longitude

# Invoke function on dataframe
df_lat_long.agg(getDistanceBetweenPoints_df, axis='columns')

# View the dataframe for values only where distance is less than or equal to 2.5◦
df_lat_long[df_lat_long['distance'] <= 2.5]


So, these are the latitudes and longitudes where distance from the given centre is less than of equal to 2.5◦. Do whatever you want to do with these